# Questions tagged [integer-programming]

For questions about mathematical optimization problems involving binary or general integer variables.

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### How can I linearise this nonlinear proportional relation constraint?

My optimisation problem has a constraint in the form \begin{array}{*{35}{l}} \text{}\hspace{16.5mm}\text{ C4:} \hspace{2mm}\sum_{u=1}^U d_{u,1}L_{u}:\sum_{u=1}^U d_{u,2}L_{u}:\cdots:\...
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### Can I solve the separation problem efficiently, when I have access to an optimization oracle?

Assume I have given a convex feasible set $X$ and I have an oracle that can optimize some linear objective function $c$ over $X$. Assume that I have given a point $r$. I want to solve the separation ...
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### What underlies intlinprog in MATLAB?

When a paper says they used the intlinprog in MATLAB to solve an integer program, what system actually does the solving? I have seen documentation about Gurobi and MATLAB: does Gurobi always provide ...
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### Flexible Job Shop with Preemption

I'm trying to solve a flexible job shop problem variant that has precedence constraints on jobs along with a few other issues. We have a MIP formulation and also a simulated annealing algorithm to ...
1 vote
148 views

### Constraint programming and scheduling issues

I have a constraint problem that I need to resolve, but I did not how know to model the problem: I have 11 employees, I will name them from $a$ to $k$: $\{a,b,c,d,e,f,g,h,i,j,k\}$. I have a small ...
611 views

### Divisibility constraint in Integer programming

I have a simple question regarding the divisibility in integer programming suppose the objective function is $\text{max}\quad x_1 + x_2$ where the constraint is that the sum of $x_1$ and $x_2$ are ...
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### confusing results of two models with different complexity

i have two models that address the same problem. the first one is : the second one is: for different instances for the same size (n=30) i found the following results ( the first column on the left ...
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### How to determine the size of a model?

I want to know about the number of variables and constraints of this formulation (exp: $o(n)$ variables and constraints or $o(n^2)$ ....). Is the number of variables $\mathcal O(n^3)$ because we have ...
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### Literature on "simcity-like" problems

As it will become apparent, my field is not operation-research and so this question will sound very naive. I am sorry for that. I have a set of "buildings" that I want to place on a small 2d ...
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### Any references to the ROADEF 2020 Challenge?

The problem description of the challenge is given here. Does anyone has some references to similar problem. I would like to participate but I don't know where to start.
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### Indicator function for integer variable with inequality constraint

I have $n$ integer variables $\vec{x}$ with the following integer programming problem. $$COST = \sum^{n-1}_{i = 0} a_i x_i + \sum^{n-1}_{j=0} b_j I(x_j > 0)$$ Here, $a_i, b_j \in \mathbb{R}_+$ ...
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### Finding bounds on a data sensitivity scenario ILP problem

This is a follow up to a problem I posted here: Modelling a data-sensitivity scenario as an ILP problem As a recap, I was interested in finding the minimum number of cells that need to be suppressed ...
425 views

### Issue in solving a large scale MIQP problem

I am solving a large scale MIQP optimisation problem at each step of a model predictive control problem. The problem description is as below. \begin{align} \min_{u} \quad (x_{k}&-x_\text{ref})^{T}...
119 views

### Condition for an integer program and its linear relaxation to have the same value

Let $A$ be a $(0,1)$-matrix where no row or column is a zero vector, and consider the following optimization programs \begin{align}(1):\min&\quad y\cdot1\\\text{s.t.}&\quad yA\ge w\\&\quad ...
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### What are the solvers that give a feasible solution within a given time?

What are the solvers that take the maximal computation time as a parameter and gives the best found feasible solution within this time.
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### Modelling a data-sensitivity scenario as an ILP problem

I am new to linear programming, and I recently came across the following exercise, which I do not know how to solve: When publishing data, it is sometimes important to "suppress" sensitive ...
74 views

### Linearizing max constraint Problem [duplicate]

I want to linearize a max constraint as below: In which x_(i,t),are binary decision variables and T is a constant. How can I linearize this constraint?
87 views

### How to find all covers and minimal covers?

Consider a constraint of type $$c_1x_1+c_2x_2+\cdots+c_nx_n\leq C$$ with $x_i$ binary. We call a cover a subset of the $n$ indices such that the sum of the corresponding coefficients is higher than ...
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1 vote
106 views

### How this problem can be defined as MultiObjective optimisation

I need to optimize the end-to-end latency of a multi-component application. Assuming that the application has 10 components, component 1-5 is hosted by device 1, and device 2 is hosting the other 5 ...
147 views

### When is there at least an integral point in a polyhedron?

This problem comes from a problem of economics. Let $x\in [0,1]^n$. $\{x_1,x_2,\ldots,x_n\}$ is partitioned into ${S_1, S_2,\ldots,S_k}$ such that $\sum_{x_i\in S_j}x_i\leq 1$ for each $1\leq j\leq k$....
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1 vote
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### Switching of decision variables to be larger than or equal to a decision variable according to an indicator variable value

I would like to seek some advice on modeling the following: I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is greater than or equal to a ...
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### Switching of decision variables to be equal to a certain decision variable according to a binary (indicator) variable

I would like to seek some advice on modeling the following: I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is to be equated to a third ...
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### Strong MIP formulations for a large-scale mixed-integer nonlinear feasibility problem

I'm trying to construct a strong MIP formulation for the following integer nonlinear feasibility problem. Informally: We have a $m \times n$ decision matrix of binary variables Each row of the matrix ...
520 views

### Formulating the conditional constraint

I want to develop a model extension of capacitated location problem. The variables are a binary $x_i$ and a continuous $Q_i$. The following condition must be satisfied: if $x_i = 0$, $Q_i$ must be ...
133 views

### Integer decision variables as index

The following problem has only two integer variables; however, they appear in the index of the parameters. Appreciate it if anyone has any efficient idea to transform it into a canonical integer ...
71 views

### Theoretical aspect of using extended formulation

If I can show a polyhedron Y is an extended formulation of polyhedron X and every extreme point in Y is integral, does that automatically imply the projection of Y onto the variable space of X gives ...
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